Many machining and forming processes are presently performed using machine tools that operate under numerical control (NC). In a typical NC machine installation, a set of programmed instructions is processed by a machine tool unit (MTU) that provides motion control signals to servomechanisms coupled to the machine tool installation. A work piece retained by the machine tool installation is thus formed into a finished part according to the processed instructions. The instructions are typically prepared by machine tool programmers who develop the instructions based upon available geometrical information for the finished part, which generally includes drawings of the part, either in paper or electronic form. The machine tool programmers also typically include process-related instructions, which may include feed rates for the work piece and even the selection of one or more forming tools such as drills, end mills, or other forming tools that are driven by the NC machine. The programmed instructions are generally encoded on a variety of transportable memory devices, which may include punched tapes, magnetic tapes or disks, optical disks, or even semiconductor memory devices, such as flash memory devices. The programmed instructions are then introduced to the MTU from the transportable memory device using a reader configured to read the transportable memory device.
The machine tool installation includes an articulated mechanism operable to move a machine tool relative to a predetermined set of coordinate axes. The articulated mechanism generally includes a plurality of interconnected kinematic joints, which may be either prismatic or rotational, that cooperatively position a machine tool relative to the work piece in a coordinated fashion. The complexity of the articulated mechanism depends upon the positional capability of the mechanism, as expressed in the number of coordinate axes (i.e. the “degrees of freedom”) that the mechanism exhibits. For example, in the well-known five-axis machine tool installation, the articulated mechanism is capable of translation in three mutually orthogonal directions, and is also capable of rotation about two rotational axes.
Under certain kinematic conditions, however, a movement imparted to one or more of the kinematic joints may fail to result in a desired movement of the machine tool relative to the workpiece, so that a decrease in the degrees of freedom present in the articulated mechanism occurs. Accordingly, the set of joint positions has positioned the machine tool at a singular point. For example, if the machine tool is an end mill, and the end mill is approximately aligned with a kinematic joint that is rotational then no movement imparted to the rotary joint is capable of changing the position of the end mill. In certain instances, relatively large excursions of the machine tool may occur along the singular axis while the machine tool is close to a singular point, which may damage the work piece and/or the machine tool installation.
In order to avoid encountering one or more singular points during a machining process, the process steps are generally sequentially planned by the machine programmer so that the machine tool does not encounter a singular point. Although this is an effective technique, known singular points may not be avoidable depending upon the machine tool installation and/or the work piece configuration. Moreover, in cases where the singular point is avoidable, the sequential plan may be excessively time consuming, which increases the production costs of the work piece.
Machines are typically specified and built to achieve a particular volumetric accuracy necessary to properly execute the intended process or job. For example, a machined part may have a surface location tolerance of +/−0.010″. It would then be necessary for the machine to be able to position the tool tip to better than +/−0.010″ within the working volume. There are two methods to achieve this.
One method is to build the machine with enough precision that the programming instructions to drive the machine assume that the machine is perfect. In this case, the positioning errors of the machine depend on how close to perfect the real machine is. To ensure that the machine is sufficiently close to perfect to meet the required tolerances, significant time and money must be spent when building the machine. Often this involves purchasing more expensive precision components, and making several measurements and mechanical adjustments to the machine during the construction and installation.
The other method is to build the machine without trying to make it close to perfect. Then, using standard metrology methods such as tracking laser interferometers, measure the “as built” condition of the machine. The difference between the as built machine and the perfect machine is then used to change the programming instructions so that the machine positions the tool within the specified tolerance. Because this allows the machine to be built with significant deviation from the perfect machine, much less time and money can be spent on construction and installation of the machine. This method of accuracy improvement is called software compensation, or command update.
However, when the machine is at or near a singularity, it will be difficult or impossible to calculate a command update to the programming instructions that improves the positioning accuracy of the tool tip without causing a large motion of the singular axis. This is undesirable because large axis motions may not be achievable in the time allocated to the move, and further may cause damage to the part or the machine. The solution is to sacrifice some accuracy for the sake of small changes to the program instruction.
In one known method, a software-based optimization program is used, that generally effects a trade-off between accuracy and joint position so that accuracy is compromised in order to maintain small joint motions. One disadvantage of this method is that the accuracy trade-off occurs even when the machine tool installation is not close to a singularity. Another disadvantage is that the method is computationally cumbersome, so that excessive computational times may be required.
What is needed are systems and methods for handling singularities in materials processing systems that employ software compensation that overcome the disadvantages of prior art systems, and are not computationally burdensome.